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一、我们先假设一个抽样数W={W(ij)|i,j∈N}, W(ij)就是比赛的进球结果,i,j分别表示主客队的进球数。+ |. O7 N6 U* x) I- A
那么,平局、主胜、客胜就有以下表达式:
+ u8 D( L M4 g( j" \8 g* k3 P1 d) y' ~A(d) = {W(ij)|i=j, i∈N, j∈N}
" ?# v$ f W. b% S$ F9 u4 zA(h) = {W(ij)|i>j, i∈N, j∈N}6 }- c" G, U. f* C; ]# [9 ^. d2 l
A(a) = {W(ij)|i 接着我们引入一个符号P(i)表示平胜负的概率,P(Ai)∈[0,1]:+ _$ L1 [8 E/ l- K0 C8 _' ~
P(i)=P(Ai), i∈{0, 1, 2}
" I2 I& ^- D5 @; @$ c; x/ y5 l二、首先来说说平手盘(即0:0Handicaps或我们经常在国外上看到的(Moneyline)
! k* g0 v3 n- T/ f6 t假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:
2 c% {8 U6 N6 S: I( K& F7 O{b(h) , 即上面所述的A(d)结果发生8 O5 i# U7 B: S
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
$ S) H' w& T: _8 E{0 , 即上面所述的A(a)结果发生, L K+ h4 m* S* A/ E+ R! c) ^
以及3 o+ l0 ~0 f2 X
{b(a) , 即上面所述的A(d)结果发生/ M. C. Y8 \3 y6 }
R(2)={0, 即上面所述的A(h)结果发生
; a2 f! h o6 d3 V1 z{O(a)*b(a),即上面所述的A(a)结果发生' m, M" n- N+ M8 U. v% G
如果O(h)表示平手盘下的主队赔率,O(a)表示平手盘下的客队赔率 _6 c, E+ x. ~- z9 V: U) T0 W1 I
那么投注主客的期望回报总数分别为- t+ T4 |4 G! J0 b
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]0 ~& l$ o E/ E9 ?) H- g4 L9 T
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
% Y7 u- E% p# L按照真实赔率(暂不包含庄家优势),我们可以认为实际投注回报与期望投注回报相等
9 w0 ?$ r( p0 `0 J$ x( S dE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)8 }! R7 b- ^& N+ A+ K) r, a' m% M
P(d)+p(h)O(h)=1
* [2 a* g6 g g. ~: g8 w7 n& zO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式' P9 R! x7 I/ Q3 E& }! ^
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a), b0 [7 I$ \% ]5 h/ v* W; `
P(d)+p(a)O(a)=1) Q- s# _6 k0 d3 d+ P5 K2 D+ Y# J
O(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式1 i8 w8 e, E7 I( p) `7 y
在极端情况下,可以认为平手盘亚洲赔率(或moneyline),就是在不发生平局结果条件下(就是公式中P(d)=0),主胜客胜概率的倒数
% c- \6 Y- v: ~1 g4 m三、半球盘的计算描述
0 |5 M) E5 d, C3 t% ]# F+ I1 `! V, ]接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)9 M5 [; C6 Z9 J' e7 p% d
还是假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:
/ {/ w1 M& o8 ?{O(h)*b(h),即上面所述的A(d)结果发生
4 ^: ~3 F! a/ N- z8 mR(1)={O(h)*b(h),即上面所述的A(h)结果发生
6 G* r8 h# q9 I8 n, g, r. S: s4 S{0 , 即上面所述的A(a)结果发生& Y1 {+ b1 ?! i, s. ?
以及
& g' W. b/ T9 F, X{0 , 即上面所述的A(d)结果发生
0 f% y& Y. r% i; U$ iR(2)={0, 即上面所述的A(h)结果发生5 h9 V* q3 \! r- m% G
{O(a)*b(a),即上面所述的A(a)结果发生
' d8 m! I2 w( r' {" @如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
8 T1 C# @3 s1 v3 I, ^2 P$ [& A6 a投注主客的期望回报总数分别为
, V0 z. T' g' @& ~! LE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
0 S+ J9 `: a2 o5 @* U, x" @E[R(2)]=P(a)*O(a)*b(a)
* a6 i- x C W' {# v, O/ n假设实际投注回报与期望投注回报相等( i! K& ]! m# ]2 k( B) k
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)' ~4 B9 s: R- g4 C u( x3 r
O(h)*[P(d)+p(h)]=12 Z5 w0 _& Q$ N& C0 V: o
O(h)=1/[P(d)+p(h)]
, V/ M. P' h: }% lE[R(2)]=P(a)*O(a)*b(a)=b(a): t8 V2 h4 T; b: F
P(a)*O(a)=1
1 S; n8 j0 H, M) F% I6 z1 t/ CO(a)=1/P(a)
# |/ k' T! W: ~& g; y- l同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
+ T4 Z j, x* l) \' v3 rO(h)=1/p(h)
3 H8 z/ c z, S0 K4 eO(a)=1/[P(d)+p(a)]
o' c. |( C% m% l1 }0 ^四、平半球盘的计算描述
% n5 Y* e M; s这个稍复杂一点( w- t5 g; m: z |' j# v& q9 V4 ^' A
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)9 a8 ^& h$ j. j( k5 U' T
还是假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额计算:' k, G1 H/ @2 U/ i9 Y. w8 p$ C
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生' \( O" x, C! v' H0 N
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
; Q# t$ r, Q' i5 j{0, 即上面所述的A(a)结果发生% N$ d, {4 i9 }2 a: u' M
以及. @$ g2 X* c/ D) y9 _
{1/2×b(a) , 即上面所述的A(d)结果发生0 z4 i/ _6 P7 k9 X
R(2)={0, 即上面所述的A(h)结果发生( A0 v3 V6 Q# x/ B, ?5 h# @
{O(a)*b(a), 即上面所述的A(a)结果发生
8 A X- h7 w- d0 @) H4 I3 }' j" H投注主客的期望回报总数分别为
% Z2 Q$ C9 F( ~" I' }/ W" A; }2 k2 }E[R(1)]=P(d)×{[O(h)+1]/2}×b(h)+P(h)×O(h)×b(h)=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))5 V& N: w: X% I% W. B7 t# A: H
E[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]. R6 f' Z& e; O5 T2 w7 P
和上面计算过程相似,得出:2 z4 w# _. `8 F' b% ~: B, b
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
4 ]' ?0 B" y" w* j- r7 V4 ]P(d)×{[O(h)+1]/2}+P(h)×O(h)=1
9 q" X5 p& I) A. h/ dO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1% u# Q3 N4 E7 Y3 j L* Z
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h)) B6 B* Y% q$ w. a
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
7 m; f) |3 H9 F0 a$ H) |8 \% F! d1/2×P(d)+P(a)*O(a)=1
: g& ~! K: `6 ]% A/ T0 |1 ^5 PO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
6 e, ?6 _/ |$ `& `! s同样主队让平半就分别是
7 A Q1 h) G9 Y! K5 P, _4 d- O* JO(h)=(1-P(d)/2)/P(h)) o1 O- M- H' r
O(a)=(1-P(d)/2)/(P(d)/2+P(a))
6 j# x( S+ Q0 f/ f3 Q0 X五、一球、两球等整数盘(这里先暂时说主队让1球的情况,0:1,Handicaps,其它可以类推的)$ }5 z& A* x6 D/ W( n" j s
可以采用类似公式,在(一)中我们分别用A(d)、A(h)、A(a)描述平局、主胜、客胜事件的发生。现在改用另外的符号代替,如B(d)、B(h)、B(a),同时除了平、胜、负概率P(i)(i=d,h,a)外,还需要引入一个一个概率值P(hX)来代表主队赢一球(X=1)、二球(X=2)...的概率,下面来进行演算8 A5 w/ a8 V2 C ?* W; U. p# X9 ?5 v
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
' ?4 Q0 s6 \0 ]4 YB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}6 w2 |3 w5 J( R; ?& M
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
% A) i( X: f+ G& S1 p1 K3 j接着,假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:
* z R2 I! c# {' P* t{b(h)*O(h) , 即上面所述的B(d)结果发生
# |; G3 W l: L0 SR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
$ T: L# N0 O" z# @1 u{0 , 即上面所述的B(a)结果发生# [. a; l; r4 v4 c$ @
以及! [# T2 X' `, y: f8 }% W4 f4 Z
{b(a) , 即上面所述的B(d)结果发生9 V; Y" P8 ?8 a; K* Y0 j
R(2)={0, 即上面所述的B(h)结果发生# I0 I# Q. w3 N! |
{O(a)*b(a),即上面所述的B(a)结果发生
5 t( S, M0 q: y y投注主客的期望回报总数分别为
9 ^0 h% X* O' M- J: I+ AE[R(1)]=P(h)*b(h)*O(h)+P(h1)*(b(h)-O(h)*b(h))=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]! q6 L7 ^3 ^: a+ }& ~, `
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
6 m/ W2 m# p9 W6 I假设实际投注回报与期望投注回报相等( a! @0 y( z; ?8 c
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
5 D1 j% `7 {' ]8 K7 x: J$ u# cP(h)*O(h)+P(h1)-P(h1)*O(h)=1* I6 R5 Q% r4 d9 u5 h5 W3 P
O(h)*(P(h)-P(h1))=1-P(h1)4 ^: w/ `! Q. J2 y1 f. a6 r- u
O(h)=(1-P(h1))/(P(h)-P(h1))
L# W) Q3 R VE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
9 m' E. N9 v x+ ]9 q. `P(h1)+O(a)-P(h)*O(a)=1
6 i# s! u3 n7 A4 m W# FO(a)*(1-P(h))=1-P(h1)1 ? h4 S0 `+ L. ^. u
O(a)=(1-P(h1))/(1-P(h))
# M5 o; @8 {+ X4 P以上(五)部分是让一球的情况,让两球以上整数盘和反过来受让整数盘是可以同样演算的。+ u+ H, Q5 O, P; s5 O5 U+ d
简单小结一球或整数盘,其实理论的演算过程不难,但是如何准确计算赢整数球的概率(P(hi)就是其中的难点,这已经涉及到如何用相对动态实力差或球差来计算各种赢球概率(是指赢1、2、3...球的概率,也可以说是赢球比分概率)的问题,使用自己数据模型里的数据来计算。 |
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